Lamar, 30, regarded as one of the most innovative rappers of his generation, kicked off the programme in New York with dancers dressed in military fatigues against the backdrop of an American flag.
He performed a medley of hits including “XXX” featuring U2, “DNA” and ending with “King’s Dead,” where dancers dressed in red hoodies mimicked being shot and falling to the floor.
The performance earned cheers and a standing ovation from the audience at Madison Square Garden.
Lamar won for best rap album, music video, rap song, rap performance and rap/sung performance, defeating fellow rapper Jay-Z and leaving him empty-handed despite going into the show with a leading eight nominations.
“It’s really about expressing yourself and putting that paint on the canvas for the next generation,” Lamar said. “Hip-hop has done that.”
He thanked Jay-Z, 48, and other veteran hip-hop artists for showing him the way, adding “Jay for president!”
R&B singer Bruno Mars also had a good night, winning three early Grammys for his album “24K Magic” and hit single “That’s What I Like.”
Alessia Cara was named best new artist. “I’ve been pretend-winning Grammys since I was a kid in my shower,” she said, accepting the award.
Jay-Z, who bared his soul on his “4:44” album, was not expected to perform on Sunday in a departure from Grammy tradition.
The Los Angeles Times quoted Grammy organisers as saying that Jay-Z, who was in the audience on Sunday, had turned down an invitation to perform.
He is competing against Lamar, Mars, Childish Gambino and New Zealand-born singer-songwriter Lorde for album of the year in a test of whether hip-hop can break a 14-year dry spell and win that top prize.
On the red carpet, dozens of musicians wore or held white roses to signal support for women’s equality and freedom from sexual harassment.
Inside the venue, pop singer Kesha, who has been battling her former record producer Dr Luke for years in US courts over allegations of emotional and sexual abuse, is to perform her defiant single “Praying.”
Dr Luke has repeatedly denied Kesha’s allegations.
Cara, Khalid and Logic will take the stage with a group of suicide survivors to perform their song “1-800-273-8255,” the telephone number of the National Suicide Prevention hotline.
